Preheat broiler. Cut eggplants diagonally into 1/4-inch-thick slices, discarding stem ends. On a lightly oiled large baking sheet arrange slices in one layer and broil 4 to 6 inches from heat until golden, about 8 minutes. Turn slices over and broil until golden, about 8 minutes. Cool eggplant slices slightly and chop coarse. In a bowl combine eggplant, shallots, and Vietnamese coriander (or alternative). In a small bowl stir together lime juice, fish sauce, sugar, and chili and pour dressing over eggplant. Toss mixture well and let stand 30 minutes to blend flavors. Arrange lettuce on a plate, overlapping leaves, and mound eggplant on tip. Serve eggplant with rice. Lettuce leaves can be used to pick up some salad.